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Superization and $$(q,t)$$-specialization in combinatorial Hopf algebras. (English) Zbl 1230.05281
Summary: We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the $$(q, t)$$-specializations of various bases. Exploiting the dendriform structures yields in particular $$(q, t)$$-analogs of the Björner-Wachs $$q$$-hook-length formulas for binary trees, and similar formulas for plane trees.

##### MSC:
 05E05 Symmetric functions and generalizations 05C05 Trees 16T30 Connections of Hopf algebras with combinatorics 18D50 Operads (MSC2010)
##### Keywords:
symmetric functions; superization process
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